Question

How far does a car travel if it accelerates from rest to 30 miles per hour (mph) in 8 seconds?

Answer 1

To calculate the distance traveled by a car when accelerating from rest to a certain speed, we need to consider the average acceleration during that time. The formula to calculate distance traveled during uniform acceleration is:

$d=\frac{1}{2}\cdot a\cdot t^2$

where:

• $d$ is the distance traveled
• $a$ is the acceleration
• $t$ is the time

In this case, we are given that the car accelerates from rest to 30 mph in 8 seconds. First, we need to convert the final speed from mph to the corresponding acceleration in feet per second squared (ft/s²). We'll assume the car starts from rest, which means the initial speed is 0 mph.

1 mph is equal to 1.46667 ft/s. Therefore, the final speed of 30 mph is equivalent to:

$v_f=30\times 1.46667=44ft/s$

Next, we can calculate the average acceleration using the formula:

$a=\frac{v_f-v_i}{t}$

where:

• $v_f$ is the final speed
• $v_i$